Various thin-film I$_2$-II-IV-VI$_4$ photovoltaic absorbers derived from kesterite Cu$_2$ZnSn(S,Se)$_4$ have been synthesized, characterized, and theoretically investigated in the past few years. The availability of this homogeneous materials dataset is an opportunity to examine trends in their defect properties and identify criteria to find new defect-tolerant materials in this vast chemical space. We find that substitutions on the Zn site lead to a smooth decrease in band tailing as the ionic radius of the substituting cation increases. Unfortunately, this substitution strategy does not ensure the suppression of deeper defects and non-radiative recombination. Trends across the full dataset suggest that Gaussian and Urbach band tails in kesterite-inspired semiconductors are two separate phenomena caused by two different antisite defect types. Deep Urbach tails are correlated with the calculated band gap narrowing caused by the (2I$_mathrm{II}$+IV$_mathrm{II}$) defect cluster. Shallow Gaussian tails are correlated with the energy difference between the kesterite and stannite polymorphs, which points to the role of (I$_mathrm{II}$+II$_mathrm{I}$) defect clusters involving Group IB and Group IIB atoms swapping across textit{different} cation planes. This finding can explain why textit{in-plane} cation disorder and band tailing are uncorrelated in kesterites. Our results provide quantitative criteria for discovering new kesterite-inspired photovoltaic materials with low band tailing.
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